Engineering, 2010, 2, 141-148
doi:10.4236/eng.2010.23020 lished Online March 2010 (http://www.SciRP.org/journal/eng/) Pub
Modeling and Investigation of the Wall Thickness Changes
and Process Time in Thermo-Mechanical Tube Spinning
Process Using Design of Experiments
Ahmad reza Fazeli Nahrekhalaji1, Majid Ghoreishi1, Ebrahim Sharifi Tashnizi2
1Mechanical Engineering Department, KNToosi University of Technology, Tehran, Iran
2Mechanical Engineering Department, Tafresh University, Tafresh, Iran
Received August 9, 2009; revised September 14, 2009; accepted September 27, 2009
Abstract
Tube spinning technology is one of the effective methods of manufacturing large diameter thin-walled
shapes. In this research, effects of major parameters of thermo mechanical tube spinning process such as
preform's thickness, percentage of thickness reduction, mandrel rotational speed, feed rate, solution treatment
time and aging treatment time on the wall thickness changes and process time in thermo-mechanical tube
spinning process for fabrication of 2024 aluminum spun tubes using design of experiments (DOE), are stud-
ied. The statistical results are verified through some experiments. Results of experimental evaluation are
analyzed by variance analysis and mathematic models are obtained. Finally using these models, input pa-
rameters for optimum production are achieved.
Keywords: Tube Spinning, Process Time, Wall Thickness Changes, Analysis of Variance (ANOVA),
Regression, Interaction Effect
1. Introduction
Tube spinning is advanced metal forming process which
is used for reducing the wall thickness and increasing the
length of tubes without changing their inside diameters.
For the tube spinning, there are two different methods,
forward and backward tube spinning, depending upon
the relative directions of the material flow and the roller
travel. In both methods, the work piece is fixed in one
position at one end and the remaining length is free to
slide along the mandrel.
In the forward tube spinning the roller move away
from the fixed end of the work piece and the work metal
flows in the same direction as the roller, usually toward
the headstock, as shown in Figure 1.
In the backward spinning of tubes, spinning metal is
extruded beneath the roller in the opposite direction of
the roller feed, usually toward the tailstock of the ma-
chine.
Kobayashi and Thomson [1] performed an approxi-
mate analysis to solve spin-forging problems of tube,
dividing the process into drawing and extrusion types.
Hasimoto [2] experimentally studied the deformation
mechanism of tube spinning with a model material (plas-
ticine) and particularly inspected the strain distribution
by using a flow function under the assumption of plan
deformation in the circumferential direction. K. M. Rajan
and K. Narasimhan [3] investigated the effects of heat
treatment of preform material on the mechanical proper-
ties of the flow formed part and the validity of using em-
pirical relations in predicting the properties of the flow
Figure 1. Metal flow and roller travel in forward and
backward spinning of tube.

A. R. F. Nahrekhalaji ET AL. 142
formed components. Y. Xu and S. H. Zhang [4] simu-
lated distributions of stress and strain rate of the defor-
mation by 3D rigid-plastic finite element method. Chang
and Wang [5] designed a new thermo mechanical treat-
ment process in the tube spinning for fabricating 2024
aluminum tubes. The designed process can be outlined in
sequential order as annealing, first spinning, solution
treatment, second spinning and aging. They indicated
that annealing and solution treatment can effectively re-
cover the ductility of the spun tube.
In this research, the influences of perform's thickness,
percentage of thickness reduction, mandrel rotational
speed, feed rate, solution and aging treatment time on
process time and wall thickness changes for fabricating
2024 aluminum tubes using DOE has been studied.
It is desirable to know the effects of the major pa-
rameters and interactive influences among the process
parameters on process time and wall thickness changes
and relationship between process time, wall thickness
changes and process parameters to obtain the best condi-
tions of parameters for optimum production.
For modeling and determining the influences of main
parameters and interaction effects among parameters of
the process on time of process and wall thickness chan-
ges, DOE method has been employed. The DOE is a stat-
istical method which is used to find the significance of
interactive effects among variables and relations among
process parameters using variance analysis. Finally, us-
ing this model and suitable time of process, input pa-
rameters has been achieved for optimum production.
2. Description of Material and
Thermo-Mechanical Process
All ductile metals are suitable for tube spinning. We have
chosen 2024 aluminum as experimental sample, because
it is suitable for tube spinning. The chemical composition
of this alloy (work metal) is presented in Table 1.
During fabrication, the property of 2024 aluminum
tubes must satisfy the spinning operation. Therefore, the
preform property requires appropriate heat treatment to
increase spin ability or to relieve residual stresses. In this
research the thermo mechanical treatment process de-
signed by S. C. Chang and C. C. Wang [5] has been em-
ployed.
Five processes of thermo-mechanical treatments which
are used in this study are as follows:
1) The original preform is annealed completely in order
to unify the microstructure and accomplish the mechani-
Table 1. The chemical compositions of aluminum alloy 2024.
Elements Si Fe CU Mn Mg Zn Cr Ti
Weight(%) 0.19 0.11 2.4 0.51 1.5 0.09 0.010.03
cal process with appropriate spinnability. The aluminum
tube annealing is conducted in temperature 410℃ for 2
hours [6].
2) The first tube spinning with 5% and 10% reduction
rate in thickness was conducted.
3) The solution heat treatment according to the refer-
ences, the solution heat treatment is performed in the
temperature of 490℃ for 60 to 100 minutes. The solu-
tion condition was so the transformed structure is recov-
ered and softened for the next operation [6].
4) The second tube spinning with 5% and 10% reduc-
tion rate in thickness was conducted.
5) The artificial aging is conducted in 190℃ for 2 or
3 hours which creates the desirable mechanical dimen-
sions and properties in the final tube.
3. Experimental Modeling
3.1. The Output Parameters
Output parameters process time and wall thickness cha-
nges measured in terms of minute and mm.
3.2. The Input Parameters
Input parameters were selected from the various param-
eters of spinning such as the properties of the work piece
material, tools, mandrel rotational speed, rigidity of ma-
chine tools, type of coolant and feed rate of rollers. The
selected parameters are:
- The initial thickness of perform part.
- The percentage of thickness reduction.
- The mandrel rotational speed.
- The feed rate of rollers.
- The time of solution treatment and aging.
3.3. The Experiment Conditions
Two rollers made of hardened steel were applied to im-
plement the experiments. The radius of roller tip was 3.5
mm, the roller diameter, 126 mm, the attack angle of
roller, 22.5˚ [8], the back angle of roller, 22.5˚ and the
internal diameter of preform was equal to the roller di-
ameter.
3.4. The Experimental Design
It is difficult and expensive to perform all experiments.
The DOE method can be employed as an efficient tech-
nique to accomplish the suitable and necessary experi-
ments with high accuracy. To investigate main and mul-
tiple interactions between parameters [7], in this study, a
fractional-factorial design was employed with two levels
for each parameter (+,–), half fraction with resolution

A. R. F. Nahrekhalaji ET AL. 143
(VI). Table 2 shows the input parameters of the process.
The procedure includes 32 experiments. The experiments
were divided into 2 blocks of 16 experiments in order to
eliminate the effects of noise factors (uncontrollable fac-
tors), environmental factors (temperature, humidity) and
errors that arises from the human sources and measure-
ment tools. Sixteen experiments were conducted in dif-
ferent days.
Since the considered levels for each of the input pa-
rameters are two levels, the number of experiments is
conducted to determine whether three levels is necessary
for each parameter or not which is called the center
points. If these points were recognized as the effective
points by the analysis of variance, then the experiments
should be performed in three levels. Table 3 indicates
the center points. Figure 2 shows the spun parts. Figure
3 shows the flow chart of the analysis.
Table 2. The parameter levels.
Parameters Low Level High Level
speed of rotational speed (rev/min)v 67 114
feed rate of rollers (mm/rev)f 0.17 0.3
percent of thickness reduction %T 5 10
initial thickness (mm)T 4 6
solution treatment time (min)ts 60 100
aging treatment time (hr)ta 3 4
Table 3. The applied center points in this study.
Run T
(mm)
T
%
V
(rev/min)
f
(mm/rev)
ts
(min)
Ta
(hr)
Δt
(mm)
t
(min)
1 4 7.5 90 0.3 80 3.5
–0.261 383.117
2 4 7.5 90 0.3 80 3.5
–0.238 383.17
3 4 7.5 90 0.3 80 3.5
–0.307 383.333
Figure 2. The spun parts.
Derivation of interactive
influences and multiple linear
equations with MINI TAB
software
P-Values for 95%
confidence level of multiple
linea
r
N
o
N
o
Yes
Yes
Figure 3. Flow chart of the analysis.
4. Analysis of the Experimental Results
The analysis of variance (ANOVA) is a statistical met-
hod to investigate the importance and effect of the pa-
rameters. After statistical calculations and implementa-
tion of the F-test on the experimental data by ANOVA,
probability values of each parameter are extracted from
the table of variance analysis. The risk level as consid-
ered as 0.05 for the ANOVA.
Once the experimental results are obtained, the coeffi-
cients and analysis of variance (ANOVA) are then cal-
culated with MINI TAB software to determine the sig-
nificance of the parameters, and the P-Values is used to
determine which parameter is most significant. The F-
ratio test is conducted to check the adequacy for the
proposed model. Through experiments, internal diameter
growth and wall thickness changes are collected and then
fed into a DOE/STAT program to construct statistical
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A. R. F. Nahrekhalaji ET AL. 144
regression equations for achieving the initializing of in-
put parameters for optimum production.
4.1. Analysis of the Experimental Results on the
Wall Thickness Changes:
After the initial variance analysis and elimination of the
unimportant parameters (with low effect coefficient) and
use of projection (due to lack of repeat), and with regards
to the calculated values of F and P for each one of the
effective parameters which is extracted from the table of
variance analysis, it can be concluded that the blocking
has no important effect on the wall thickness changes (P
= 0.830). Therefore we can eliminate this blocking from
the variance analysis, and analyze the experiments again
(Table 4). The risk level of less than 0.05 for parameters
in Table 4 shows that the related parameter is significant.
Also, in Table 4 it can be observed that the center points
have no effect (P = 0.94).
Therefore, the two levels design is appropriate and we
do not need to consider the effective parameters in 3 or
more levels. The R squared and the adjusted R squared
are shown in bottom of the Table 4. Also, the lack of
fitness is insignificant which shows the adequacy of the
developed model. Figure 4 indicates the residuals analy-
sis graph of the regression model. As it observed, the
residuals have a normal distribution.
Table 4. The variance analysis (ANOVA) for the wall thick-
ness changes.
Parameters DOF Adj SS Adj MS Fo P
Main Effects
2-Way Interactions
3-Way Interactions
Curvature
Residual Error
Lack of Fit
Pure Error
Total
6
8
3
1
16
14
2
34
2.828
0.107
0.047
0.0
0.0215
0.019
0.002
0.4713
0.0134
0.0157
0.0
0.0013
0.0013
0.0012
350.10
9.99
11.68
0.0
1.10
0.0
0.0
0.0
0.94
0.57
R-Sq = 99.29% R-Sq(adj) = 98.49%
Figure 4. Residuals analysis graph of the regression model.
Figure 5 shows the graphs of each input parameter
effect on the wall thickness changes. Also, Figure 6 in-
dicates interactions effects of the parameters on the wall
thickness changes.
Figure 6 shows that for the wall thickness changes
there are significant interactive influences among initial
thickness and percentage of thickness reduction, feed
rate of rollers and solution treatment time, mandrel rota-
tional speed and aging treatment time.
Also, thinner of initial thickness, small percentage of
thickness reduction, slower mandrel rotational speed,
lower solution treatment time and higher of feed rate of
rollers lead to smaller wall thickness changes.
Mean of wall thickness changes
Figure 5. The graphs of mean parameter effect on the wall
thickness changes.
Figure 6. The graphs of the parametric interactions effect
on the wall thickness changes.

A. R. F. Nahrekhalaji ET AL. 145
Figure 7 summarizes the initial thickness on the wall
thickness changes of tube spun at percentage of thickness
reduction. The result shows that decrease of initial thick-
ness combined with the decrease of percentage of thick-
ness reduction produces small wall thickness changes of
the spun tube.
Reasonably, the thicker the initial thickness and dee-
per the percentage of thickness reduction , the more en-
ergy is required for the material to deform and the de-
formation is contributed to the vicinity of the inner sur-
face as the material flows in the radial direction and wall
thickness changes tube spun increase.
Figure 8 shows effect of mandrel rotational speed on
the wall thickness changes of tube spun at various initial
thicknesses. Reasonably, at the slower mandrel rotational
speed, the deformation is confined only to the vicinity of
the outer surface as the wall thickness changes of tube
spun decrease.
4.2. Analysis of the Experimental Results on the
Process Time
After the initial analysis of variance, elimination of the
unimportant parameters (with low effect coefficient) and
using projection (because of the few iterations), it can be
concluded that the blocking has no important effect on the
process time (P = 0.369), therefore we can eliminate this
blocking from the analysis of variance and analyze the
Figure 7. Effect of the initial thickness on the wall thickness
changes of tube spun at percentage of thickness reduction.
Figure 8. Effects of mandrel rotational speed on the wall
thickness changes of tube spun at various initial thick-
nesses.
experiments again (Table 5). Also it means that the ex-
perimental condition is fixed and the out-of-control pa-
rameters such as temperature and humidity have no effect
on the experiments.
After elimination of blocking and applying the analysis
of variance (Table 5), we observed that the center points
have effect (P = 0). Therefore, the design of experiments
is not correct and there is need to consider the mean input
parameters in 3 or more levels. Another parameter which
is very important in table ANOVA is the lack of fitness
which shows the correctness of regression analysis of the
process time. The ineffectiveness of this parameter (P =
0.312) guarantees the integrity of the Analysis.
Figure 9 indicates the residuals analysis graph of the
regression model. As it observed, the residuals have a
normal distribution.
Figure 10 shows the graphs of each input parameter’s
effect on the process time. Also, Figure 11 indicates
interaction effects of the parameters on the process time.
As it was shown any parameter has not interaction ef-
fects on the others, then each parameter is considered
through the mean effect graph. Also, this graph indicates
that all input parameters affect process time. According to
Figure 9, the process time decreases as a result of in-
creasing the initial thickness, mandrel rotational speed,
feed rate of rollers and decreasing of the percentage of
Table 5. The variance analysis (ANOVA) for the process
time.
Parameters Dof Adj SS Adj MS Fo P
Main Effects
2-Way Interactions
3-Way Interactions
Curvature
Residual Error
Lack of Fit
Pure Error
Total
6
11
5
1
11
9
2
45184.7
96.9
3.8
4.5
34
0.3
0.3
0.0
7530.79
8.81
0.77
4.50
0.03
0.03
0.01
26098
305.2
26.63
155.8
2.56
0.0
0.0
0.0
0.0
0.312
R-Sq = %100.00 R-Sq(adj) = %100.00
Figure 9. Residuals analysis graph of the regression model.
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A. R. F. Nahrekhalaji ET AL. 146
Figure 10. The graphs of mean parameter effect on the process time.
Figure 11. Interaction effects of the parameters on the process time.
thickness, solution treatment time and aging treatment
time.
5. The Predictor Model of Wall Thickness
Changes and Process Time
Finally, two hierarchical models were developed for wall
thickness changes and process time by multiple linear
regression technique. The insignificant terms were re-
moved from the model and the final models were devel-
oped with significant terms which were determined by
ANOVA Equation (1) for wall thickness changes and (2)
for process time.
)(109.0)%(1692.0)(0523.0
)(0286.0)(0006.0)(0014.0
)(0032.0)(00003.0)(%0004.0
)(7415.0)(%846.0)(101.2
)%(0525.0)(249.0)(4012.0)(0066.0
)(1253.13)(6239.0)(%1163.06194.21
tsfTfTTtsf
taTVTtats
tsTtsVtsT
taffTfT
TTtstaV
fTTt











(1)

A. R. F. Nahrekhalaji ET AL. 147
)(0147.0
)(75.0)%(78.54)(157.0
)(253)(0001.0)(%45.1)%(14.0
)(%0066.0)(75.33)(68.1
)(20.14)(%2)(81.266)(29.71
)(31.1296)(014.1)(73.5936.6602(min)
tsVT
tatsTfTTtsV
VTtsVfTTT
VTfTfV
VTTfV
Ttstat






(2)
In order to check the reliability of the equations in-
duced through regression analysis, independent experi-
ments with process parameters different from the 35 as-
signed experiments, are selected. Table 6 demonstrates
the comparison of the prediction data derived from Equa-
tion (1) with the experimental results. The verification of
the results shows that the developed models have ac-
ceptable error. From the results, it is sound that, the pre-
diction error ranged within 13.63%.
The verification of the results, Table 7, shows that the
developed models have acceptable error. From the results,
it is sound that, the prediction error ranged within 1.11%.
6. Conclusions
In the present study, the thermo mechanical tube spin-
ning process has been optimized by selection of signifi-
cant input parameters including the initial thickness of
preform, percentage of thickness reduction, mandrel ro-
tational speed, feed rate of rollers, solution treatment
time and aging treatment time. Finally, by means of
ANOVA, the main effects of the input parameters and
their interactions on the wall thickness changes and
process time were determined. Based on the statistical
analysis of the experimental data the following conclu-
sions can be obtained.
1) With regards to the variance analysis and the effect
of interactions between the input parameters, it can be
concluded that with the thinner initial thickness, small
reduction rate of thickness, lower solution treatment time,
slower mandrel rotational speed and higher feed rate of
rollers, the wall thickness changes decrease, as a result
the wall thickness changes reaches a suitable level.
2) Also for process time, it was shown any parameter
has not interaction effects on the others, and each pa-
rameter is considered through the mean effect graph.
Also, all input parameters affect process time and the
process time decreases as a result of increasing the initial
thickness, mandrel rotational speed, feed rate of rollers
and decreasing of the percentage of thickness, solution
treatment time and aging treatment time.
3) In the thermo mechanical tube spinning process,
blocking have insignificant effects on the wall thickness
changes and process time. It means that noise factors
(uncontrollable) have no effect on spinning process.
4) In the thermo-mechanical tube spinning process
center points have insignificant effects on the process
time and the wall thickness changes. It means that proc-
ess can be modeled with two levels for each input pa-
rameters.
5) Finally, with regards to the large number of effec-
tive parameters in the tube spinning thermo-mechanical
process, consideration of the tube spinning through the
design of experiments is shown to be the efficient
method for achieving the acceptable results.
Table 6. Experiments that were implemented to affirm the equation relate to the wall thickness changes.
Parameters Results
Run
T %T V f ts ta Exp. Mod.
Error (%)
1 6 8 820.3 90 3.5 -0.45 -0.48 6.25
2 4 7 940.17 70 3.75 -0.218 -0.24 9.16
Table 7. Experiments that were implemented to affirm the equation relate to the process time.
Parameters Results
Run
T %T V f ts ta Exp. Mod.
Error (%)
1 6 8 820.3 90 3.5 379 380.6 0.26
2 4 7 940.17 70 3.75 395.4 397 0.4
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A. R. F. Nahrekhalaji ET AL. 148
7. References
[1] S. Kobayashi and E. G. Thomson, “Theory of spin forg-
ing,” China Institute for Radiation Protection Annalen,
Vol. 10, pp. 114-123, 1961-1962.
[2] H. Hasimoto, S. Kita, T. Shibasaka and S. Yoshida, “On
the deformation in tube spinning,” Himegi Industrial
University Report, No. 33A, 1980.
[3] K. M. Rajan and K. Narasimhan, “Effect of heat treat-
ment of prefom on the mechanical properties of flow
formed AISI 4130 Steel Tubes—a theoretical and ex-
perimental assessment,” Journal of Materials Processing
Technology, Vol. 125-126, pp. 503-511, 2002.
[4] Y. Xu and S. H. Zhang, “3D rigid-plastic FEM numerical
on tube spinning,” Journal of Materials Processing Tech-
nology, Vol. 113, pp. 710-713, 2001.
[5] S. C. Chang and C. C. Wang, “Fabrication of 2024 alu-
minum spun tube using a thermo mechanical treatment
process,” Journal of Materials Processing Technology,
Vol. 108, pp. 294-299, 2001.
[6] American Society for Metals Handbook, Vol. 4: Heat
Treating, American Society for Metals International, 2nd
edition, 1994.
[7] D. C. MontGomery, “Design of experimentals & statis-
tica modeling,” McGrow Hill Incorporation, New York,
2005.
[8] Z. E. Ma, “Optimal angle of attack in tube spinning,”
Journal of Materials Processing Technology, Vol. 37, pp.
217-224, 1993.